This paper studies a four-field hyperbolic PDE model that was recently introduced by Bemfica, Disconzi, and Noronha for the pure radiation fluid with viscosity, and asks whether shock waves admit continuous profiles in this description. The model containing two free parameters $\mu$, $\nu$ and being causal whenever one chooses $(\mu ,\nu )$ from a certain range $\mathcal{C}\subset {\mathbb{R}}^2$, this paper shows that for any choice of $(\mu ,\nu )$ in the interior of $\mathcal{C}$, there is a dichotomy in so far as (i) shocks of sufficiently small amplitude admit profiles and (ii) certain other, thus necessarily nonsmall, shocks do not. This finding does not preclude the possibility that if one chooses $(\mu ,\nu )$ from a specific part $\mathcal{S}$ of the boundary of $\mathcal{C}$, the dichotomy disappears and all shocks have profiles; the parameter set $\mathcal{S}$ corresponds to the “sharply causal” case, in which one of the characteristic speeds of the dissipation operator is the speed of light.

中文翻译：

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Bemfica-Disconzi-Noronha 模型中不存在和存在冲击剖面

本文研究了 Bemfica、Disconzi 和 Noronha 最近为具有粘性的纯辐射流体引入的四场双曲线 PDE 模型，并询问在此描述中冲击波是否允许连续剖面。包含两个自由参数的模型$\mu$, $\nu$ 并且无论何时选择都是因果关系 $(\mu ,\nu )$ 从一定范围 $\mathcal{C}\subset {\mathbb{电阻}}^2$，本文表明对于任何选择 $(\mu ,\nu )$ 在内部 $\mathcal{C}$，就 (i) 幅度足够小的激波承认轮廓和 (ii) 某些其他的，因此必然是非小激波而言，存在二分法。这一发现并不排除一种可能性，如果人们选择$(\mu ,\nu )$ 从特定部分 $\mathcal{秒}$ 的边界 $\mathcal{C}$，二分法消失，所有冲击都有轮廓；参数集$\mathcal{秒}$ 对应于“尖锐因果”的情况，其中耗散算子的特征速度之一是光速。